2,682 research outputs found
Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes
A detailed study is presented of the counterrotating model (CRM) for
electrovacuum stationary axially symmetric relativistic thin disks of infinite
extension without radial stress, in the case when the eigenvalues of the
energy-momentum tensor of the disk are real quantities, so that there is not
heat flow. We find a general constraint over the counterrotating tangential
velocities needed to cast the surface energy-momentum tensor of the disk as the
superposition of two counterrotating charged dust fluids. We then show that, in
some cases, this constraint can be satisfied if we take the two counterrotating
tangential velocities as equal and opposite or by taking the two
counterrotating streams as circulating along electro-geodesics. However, we
show that, in general, it is not possible to take the two counterrotating
fluids as circulating along electro-geodesics nor take the two counterrotating
tangential velocities as equal and opposite. A simple family of models of
counterrotating charged disks based on the Kerr-Newman solution are considered
where we obtain some disks with a CRM well behaved. We also show that the disks
constructed from the Kerr-Newman solution can be interpreted, for all the
values of parameters, as a matter distribution with currents and purely
azimuthal pressure without heat flow. The models are constructed using the
well-known "displace, cut and reflect" method extended to solutions of vacuum
Einstein-Maxwell equations. We obtain, in all the cases, counterrotating
Kerr-Newman disks that are in agreement with all the energy conditions.Comment: 22 pages, 7 figures, Late
Axially Symmetric Post-Newtonian Stellar Systems
We introduce a method to obtain self-consistent, axially symmetric, thin
disklike stellar models in the first post-Newtonian (1PN) approximation. The
models obtained are fully analytical and corresponds to the post-Newtonian
generalizations of classical ones. By introducing in the field equations
provided by the 1PN approximation a known distribution function (DF)
corresponding to a Newtonian model, two fundamental equations determining the
1PN corrections are obtained, which are solved using the Hunter method. The
rotation curves of the 1PN-corrected models differs from the classical ones
and, for the generalized Kalnajs discs, the 1PN corrections are clearly
appreciable with values of the mass and radius of a typical galaxy. On the
other hand, the relativistic mass correction can be ignored for all models.Comment: 13 pages, 4 figures, to be published at Rev.Integr.Temas Ma
Distribution functions for a family of axially symmetric galaxy models
We present the derivation of distribution functions for the first four
members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006),
which represent a family of axially symmetric galaxy models with finite radius
and well behaved surface mass density. In order to do this we employ several
approaches that have been developed starting from the potential-density pair
and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751,
1976) we obtain some distribution functions that depend on the Jacobi integral.
Now, as this method demands that the mass density can be properly expressed as
a function of the gravitational potential, we can do this only for the first
four discs of the family. We also find another kind of distribution functions
by starting with the even part of the previous distribution functions and using
the maximum entropy principle in order to find the odd part and so a new
distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217,
1986). The result is a wide variety of equilibrium states corresponding to
several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in
Rev. Acad. Colomb. Cienc. Ex. Fis. Na
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